Percentage Tricks and formulas

Percentage Important Aptitude Formulas:

1. By a certain percent, we mean that
many hundredths. Thus x percent means x hundredths, written as x%.

To express x% as a fraction:We
have, x% = x/100.

Thus, 20% =20/100 =1/5;

48% =48/100 =12/25, etc.

2.
Percentage increase = (increase/original) × 100

3.
Percentage decrease = (decrease/original) × 100

4. Increased
value at rate of x% after time‘t’ be

Increased value = Present
value × [(100 + x)/100]t

Decreased value = Present
value × [(100 - x)/100]t

5. Initial
value that is increased to present value at the rate of x% in time t, then

Initial value = present value ×
[100/(100 + x)]t

6. Initial
value that is decreased to present value at the rate of x% in time t, then

Initial value = present value ×
[100/(100 - x)]t

(II) Results on Population:

Let the
population of the town be P now and suppose it increases at the rate of R% per
annum, then:

1. Population after n years = P × [1 + (R/100)]n

2. Population n years ago = P/[1 + (R/100)]n

(III).
Results on Depreciation:

Let the
present value of a machine be P. Suppose it depreciates at the rate R% per
annum. Then,

1. Value of the machine after n years = P
× [1 - (R/100)]n

2. Value of the machine n years ago = P/[1
- (R/100)]n

(IV). If
A is R% more than B, then B is less than A by [(R/(100 + R)) × 100]%.

If A is R% less than B, then B is more
than A by [(R/(100 - R)) × 100]%.

Example: 01

If the
sales tax reduced from 3½ % to 3⅓ %, then what difference does it make
to a person who purchases an article with market price of Rs. 8400?

Solution:

Required difference = [3½ % of Rs.8400] –
[3⅓ % of Rs.8400]

= [(7/2) - (10/3)]
% of Rs.8400 =1/6 % of Rs.8400

= Rs. [(1/6)
× 8400] × (1/100) = Rs. 14.

Example: 02

A man calculates that if he lets his house
for Rs 80 per month, he would earn 7½ % p.a on his outlay after allowing for repairs.
Actually he is able to let it for Rs. 76 p.m and had to spend Rs. 60 more on
repairs. He thus gets only 6% p.a on his outlay. Find the outlay?